What is the best point to point route/mode (train or bus) from Varenna to Bolzano?
db,
Use the trains as they're much faster. Your route is very easy.....
- Varenna-Esino to Milano Centrale (about an hour)
- Milano Centrale to Verona Porta Nuova (about 1H:20M)
- Verona P.N. to Bolzano (about 1H:30M)
The travel times will vary somewhat, depending on which trains you choose. For example, there are departures from Varenna at 07:37 and 10:37 (and later) which have a total travel time of 4H:53M and that's about the quickest travel times. Check the Trenitalia website for details.
When you buy your tickets, you'll likely be given two or three tickets, which are printed on card stock. As some of the trains on that route will be Regionale, DON'T forget to validate prior to boarding the train on the day of travel, or you'll risk hefty fines, which will be collected on the spot!
I'm not aware of a direct or semi-direct bus on that route. You could rent a car, if you want to explore the mountains, but not to save time or money.